Modular synth with virtual sound modeling, connects to a PC. Nitzer Ebb's Bon Harris brought his along to use on Adore. Also used on Billy's solo album.
[info on Vintage Synth Explorer]

Billy's Nord went up on the Pumpkins' official eBay account on July 13, 2011, but ended on the 23rd at $740 with the reserve not met. A Nord Rack 2 also went up at the same time, but its reserve was not met either. The keyboard went up again on July 27 with a starting price of $700 and no reserve, and was won at $755 on August 3rd. The accompanying text read as follows:

Nord Modular Classic Keyboard synth with modular abilities using virtual sound modeling. The keyboard houses the synth engine and all DSP processors. Used on Billy Corgan's 2005 The Future Embrace album and tour. Serial number: MA20081584. Unit is fully functional and comes with power cord attached. No other cords or manuals are included. A certificate of authenticity is included. Information can be found on the Clavia website. http://www.vintagesynth.com/clavia/nordmod.php